1²-2²+3²-4²+5²…-98²+99²
=(1+2)(1-2)+(3+4)(3-4)+.+(97+98)(97-98)+99²
=-(1+2)-(3+4)-.-(97+98)+99²
=-(1+2+3+4+...+97+98)+99²
=-(1+98)*98/2+99²
=-99*49+99²
=99*(99-49)
=99*50
=4950
1²-2²+3²-4²+5²…-98²+99²
=(1+2)(1-2)+(3+4)(3-4)+.+(97+98)(97-98)+99²
=-(1+2)-(3+4)-.-(97+98)+99²
=-(1+2+3+4+...+97+98)+99²
=-(1+98)*98/2+99²
=-99*49+99²
=99*(99-49)
=99*50
=4950